It wouldn't be too weird for something like:
Interviewer: "Anything else you would like to mention?"
You:"As my little brother has been undergoing months of treatment here for his Hosgkinsretinosarcoblastoma, I have seen the care and compassion of your medical students, residents, and attendings. Their excellence further inspires me. I have also had to be support for him and my mother through this, and hope to continue that in the future. In addition, I have seen first hand the effects of your cutting edge research in NanoMolecule27, which is related to MicroParticle32, about which I have done extensive research in undergrad...Therefore, I think I am an excellent fit for this institution."
It would be pretty weird for something like:
Interviewer: "Do you have any ties to the area?"
You:"My second cousin is being treated for herpes here."
Interviewer: *Silence*
You: "Oh, and once my uncle had a rectal abscess drained here."
Interviewer *Blink* *Blink*
You: "So, I'd say I have some pretty significant ties here."
It's all in how you sell it. But I think unless it demonstrates you have a significant need to be in the area or allows you speak to specific things you know about the institution, it probably doesn't matter.